Cooper pair splitting in ballistic ferromagnetic SQUIDs

TL;DR

This paper investigates how ballistic ferromagnetic SQUIDs with spin filtering enable pure Cooper pair splitting, revealing unique current-phase behaviors and flux periodicity due to system geometry and spin filter misorientation.

Contribution

It introduces a model of ballistic ferromagnetic SQUIDs with spin filtering, analyzing how geometry and spin filter orientation affect Josephson current and SQUID characteristics.

Findings

Josephson current is due to split Cooper pairs in spin-filtered arms.

Current-phase relation can become a pi-junction or have additional zero crossings.

Magnetic flux periodicity is doubled compared to conventional SQUIDs.

Abstract

We consider ballistic SQUIDs with spin filtering inside half-metallic ferromagnetic arms. A singlet Cooper pair cannot pass through an arm in this case, so the Josephson current is entirely due to the Cooper pair splitting, with two electrons going to different interferometer arms. In order to elucidate the mechanisms of Josephson transport due to split Cooper pairs, we assume the arms to be single-channel wires in the short-junction limit. Different geometries of the system (determined by the length of the arms and the phases acquired by quasiparticles during splitting between the arms) lead to qualitatively different behavior of the SQUID characteristics (the Andreev levels, the current-phase relation, and the critical Josephson current) as a function of two control parameters, the external magnetic flux and misorientation of the two spin filters. The current-phase relation can change its amplitude and shape, in particular, turning to a pi-junction form or acquiring additional zero crossings. The critical current can become a nonmonotonic function of the misorientation of the spin filters and the magnetic flux (on half of period). Periodicity with respect to the magnetic flux is doubled, in comparison to conventional SQUIDs.